According to a famous Middle Eastern folk tale Pythagoras was one day walking past a blacksmith's workshop when he heard the sounds of different hammers pounding the anvil. Mostly they just made a noise but every so often he noticed they fell into a sequence that produced something special.
When he went inside he discovered that the hammers were all of different sizes and when he measured them, all but one had a particular mathematical relationship. If these hammers struck the anvil in sequence, the notes they produced had a harmony to them. This was because one turned out to be half the weight of the biggest, another was two-thirds the weight and the next was four-fifths the size of the largest hammer.
In this way Pythagoras is thought to have defined the octave and how it relates to the third and the perfect fifth. These are the key musical intervals that, for centuries, dictated the entire grammar of Western tonality.
Sounds like Pythagoras had a miraculous agitation!
